displace the dominant labor theory of value, was part of the network of
mathematician-logicians preceding Russell. The shift in organizational base of
these networks in the 1870s was responsible for the revolution in economic
method. Economics had long existed as a practical discipline in connection
with political doctrines and movements. Jevons promoted a paradigm revolu-
tion as the field became academicized and de-politicized; economics found its
slot in the universities as a broadening of the contents of moral philosophy,
hybridized with mathematics. Jevons got his chair at Manchester (1866) in
logic and political economy a few years before his development of marginal
utility; as a pupil of the mathematical networks, he colonized the field for
mathematical methods. Sidgwick, too, like most other Utilitarians, also wrote
on economics. His lineage would extend into the following generation with
both G. E. Moore and Keynes.
The Logicism of Russell and Wittgenstein
At Cambridge after the university reform, there occurred a confluence of all
the major trends of British intellectual life: the algebraist-logicians; the Utili-
tarians; but also the Idealists, under whose auspices the newly reformed uni-
versities passed from religious to secular control. Russell epitomizes the result-
ing transformation, for he was involved in every aspect of these networks. His
teachers (Ward, Stout) and early friends (McTaggart, Moore) were Idealists,
but there were also Utilitarian connections.^16 On the algebra–mathematical-
logical side, Russell not only inherited the Cambridge tradition but was also
an aggressive internationalist, attending the new mathematical congresses led
by Cantor and Hilbert and importing the latest techniques. These he promoted
as solutions to long-standing puzzles that Idealists had used for mystifying
science. Here Russell continued the tradition of British reformers who had been
touting German advances ever since the Humboldtian revolution. Russell was
a central figure in a group which carried off several revolutions at once. We
take up first the mathematical-logical strand and its conjuncture with the
anti-Idealist break; later we will return to the post-Utilitarian movement and
ordinary language philosophy, which emerged out of this same network matrix
and indeed in the same circle of friends.
In the late 1890s Cayley’s pupil Whitehead extended the British algebraic
tradition into a generalized treatment of logic.^17 His pupil Russell, in turn,
writing in 1897 on the foundations of geometry, classified the various non-
standard geometries around their axiomatic properties. In 1903 Russell’s Prin-
ciples of Mathematics took on the even more ambitious task of founding all
of mathematics and physics upon a small number of concepts of symbolic logic.
It brought together the logic of classes, Dedekind’s and Cantor’s theories of
The Post-revolutionary Condition^ •^709